This paper investigates the design of a priority rule in a multi-product disassembly environment. Specifically, it is concerned with product scheduling by which the inventory control of disassembled parts can be incorporated into a priority rule to reduce part lead times. The part lead time consists of two components: flow time and supply delay. The primary focus of the paper is on the development of a disassembly priority rule that aims to reduce the supply delay. We propose a priority rule, called Minimum Distance (MD) rule, to improve the supply delay performance. Finally, we provide a comparative analysis on the performance of traditional rules and the new rule proposed in this paper via a simulation model.